In many applications, it can be very useful to identify groups or clusters of objects such that objects in the same cluster are similar while objects in different clusters are dissimilar. Such identification of groups is referred to as “clustering.” Clustering has been used extensively to identify similar web-based objects. Web-based objects may include web pages, images, scientific articles, queries, authors, news reports, and so on. For example, when a collection of images is identified by a image search engine, the search engine may want to identify clusters of related images. The search engine may use various well-known algorithms including K-means, maximum likelihood estimation, spectral clustering, and so on. These algorithms generate clusters of homogeneous objects, that is, objects of the same type (e.g., generate clusters of images only or clusters of web pages only).
Recently, attempts have been made to cluster highly interrelated heterogeneous objects such as images and their surrounding text, documents and terms, customers and their purchased items, and so on. The goal of heterogeneous clustering is to identify clusters that contain related objects of two types. The use of homogeneous clustering on objects of each type separately may not be an acceptable basis for not heterogeneous clustering because the similarities among one type of objects sometimes can only be defined by the other type of objects. One attempt at co-clustering objects of two types tries to extend traditional spectral clustering algorithms using a bipartite spectral graph clustering algorithm to co-cluster documents and terms simultaneously. A similar attempt has been made at co-clustering heterogeneous objects in the field of biology and image processing. Some attempts have been made at high-order co-clustering, that is, co-clustering objects of more than two data types. However, such attempts have not used in an effective objective function nor is there sufficient evidence of the effectiveness of the iterative algorithms used by these attempts.